Field
Embodiments described herein relate generally to spectral projection data, and more specifically to material decomposition of spectral projection data.
Description of the Related Art
Projection data can be used for many applications, including: computed tomography, radiography, mammography, and tomosynthesis. Projection data reveals the internal structure of an object by transmitting radiation through the object and detecting changes in the transmitted radiation relative to when the object is absent. In absorption imaging the projection data represents Radon transforms of the attenuation along the rays traced by the radiation. Computed tomography uses projection data at a series of projection angles to reconstruct an image of the internal structure of the object.
Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray source, irradiates the body from one side. A collimator, generally adjacent to the X-ray source, limits the angular extent of the X-ray beam, so that radiation impinging on the body is substantially confined to a planar region (i.e., an X-ray projection plane) defining a cross-sectional slice of the body. At least one detector (and generally many more than one detector) on the opposite side of the body receives radiation transmitted through the body in the projection plane. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector. In some implementations a multi slice detector configuration is used, providing a volumetric projection of the body rather than planar projections.
Typically the X-ray source is mounted on a gantry that revolves about a long axis of the body. The detectors are likewise mounted on the gantry, opposite the X-ray source. A single cross-sectional image of the body is obtained by taking projective attenuation measurements at a series of gantry rotation angles, and processing the resultant data using a CT reconstruction algorithm. To obtain multiple cross-sectional images or a three-dimensional image, the X-ray sources and detectors must be translated relative to the body. The body is translated relative to the gantry, and a plurality of views may be acquired, each such view comprising attenuation measurements made at a different angular and/or axial position of the source. In some CT systems, the combination of translation of the body and the rotation of the gantry relative to the body is such that the X-ray source traverses a spiral or helical trajectory with respect to the body. The multiple views are then used to reconstruct a CT image showing the internal structure of the slice or of multiple such slices.
Because X-ray CT is the most common form of CT in medicine and various other contexts, the term computed tomography alone is often used to refer to X-ray CT, although other types exist (such as positron emission tomography and single-photon emission computed tomography). Other terms that also refer to X-ray CT are computed axial tomography (CAT scan) and computer-assisted tomography.
In one example of X-ray CT, X-ray slice data is generated using an X-ray source that rotates around the object; X-ray sensors are positioned on the opposite side of an image object from the X-ray source. Machines rotate the X-ray source and detectors around a stationary object. Following a complete rotation, the object is moved along its axis, and the next rotation started.
Newer machines permit continuous rotation with the object to be imaged slowly and smoothly slid through the X-ray ring. These are called helical or spiral CT machines. Systems with a very large number of detector rows along the axial direction perpendicular to the rotation axis are often termed cone beam CT, due to the shape of the X-ray beam.
Making projective measurements at a series of different projection angles through the body, a sinogram can be constructed from the projection data, with the spatial dimension of the detector array along one axis and the time/angle dimension along the other axis. The attenuation resulting from a particular volume within the body will trace out a sine wave oscillating along the spatial dimension of the sinogram, with the sine wave being centered on the axis of rotation for the CT system. Volumes of the body farther from the center of rotation correspond to sine waves with greater amplitudes. The phase of each sine wave in the sinogram corresponds to the relative angular positions around the rotation axis. Performing an inverse Radon transform (or an equivalent image reconstruction method) reconstructs an image from the projection data in the sinogram, where the reconstructed image corresponding to a cross-sectional slice of the body.
Conventionally, energy-integrating detectors have been used to measure CT projection data. Now, recent technological developments are making photon-counting detectors (PCDs) a feasible alternative to energy-integrating detectors. PCDs have many advantages including their capacity for performing spectral CT. To obtain the spectral nature of the transmitted X-ray data, the PCDs split the X-ray beam into its component energies or spectrum bins and count a number of photons in each of the bins.
Many clinical applications can benefit from spectral CT technology, which can provide improvement in material differentiation and beam hardening correction. Further, semiconductor-based PCDs are a promising candidate for spectral CT, which is capable of providing better spectral information compared with conventional spectral CT technology (e.g., dual-source, kVp-switching, etc.).
One advantage of spectral CT, and spectral X-ray imaging in general, is that materials having atoms with different atomic number Z also have different spectral profiles for attenuation. Thus, by measuring the attenuation at multiple X-ray energies, materials can be distinguished based on the spectral absorption profile of the constituent atoms (i.e., the effective Z of the material). Distinguishing materials in this manner enables a mapping from the spectral domain to the material domain. This mapping is conventionally referred to as material decomposition.
Material decomposition of spectral CT data is possible because the attenuation of X-rays in biological materials is dominated by two physical processes—photoelectric and Compton scattering. Thus, the attenuation coefficient as a function of energy can be approximated by the decompositionμ(E,x,y)=μPE(E,x,y)+μC(E,x,y),where μPE(E,x,y) is the photoelectric attenuation and μC(E,x,y) is the Compton attenuation. This attenuation coefficient can be rearranged instead into a decomposition of a material 1 (e.g., a high-Z material such as bone) and a material 2 (e.g., a low-Z material such as water) to becomeμ(E,x,y)≈μ1(E)c1(x,y)+μ2(E)c2(x,y),where c1,2(x,y) is a spatial function describing the concentrations of material 1 and material 2 located at position (x,y).
While semiconductor-based PCDs provide unique advantages for spectral CT, they also create unique challenges. For example, without correcting for nonlinearities and spectral shifts in the detector response, images reconstructed from semiconductor-based PCDs can have poorer image quality. The detector response corrections are in response to pileup, ballistic deficit effects, polar effects, characteristic X-ray escape, and space-charge effects.
The combination of detector response correction and material decomposition creates a complex problem. There are iterative methods of accounting for the detector response and decomposing the projection data into material components referred to as projection lengths. However, in some cases the methods can iterate to an incorrect solution corresponding to a local rather than global minimum of the problem formulation. Therefore, beginning the iterative methods with a well-chosen initial estimate of the projection lengths is important to obtaining the optimal projection lengths.